Université d'Ottawa University of Ottawa

Semiconductor Quantum Dot Lasers

by Karin Hinzer

Thesis submitted to the Faculty of Graduate Studies and Research in partial fulfilhent of the requirements for the degree of

Master of Science in Physics

Department of Phys ics University of Ottawa

Ottawa-Carleton Institute for Physics Ottawa, Canada

1998

Q Karin Hinzer, 1998

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Stirnulated emission in semiconductor quantum dot (QD) laser structures is

demonstrated- Red-enaitting, self-assembled QDs of highljP saainecl InAlAs were _pvm

by molecula. beam epitaxy on Ga& substrates. Carriers injected elecaically h m the

doped regions of separate confinement heterosîructrrres thermalized efficiently into the

zero-dimensional QD states, and stimulated emission at - 707 nm is observed at 77 Kelvin with a threshold cment of 175 mifiamperes for a 6 0 - p by 4 0 0 - p broad area

laser. A measured extemal quantum efficiency of -8.5 % at low temperature with a peak

power greater than 200 milliwatts dernonstrate good size distribution and high gain in

these hi&-quaiity QDs.

Results fiom structures with contact layerç designed to improve carrier

confinement, show a lower threshold current densïty at low temperatures and are able to

- operate up to room temperature. At low temperatures (4-50 K), stimulated emission

occurs via excited state of the QDs, followed by a gradual stimulated transition h m the

excited states to the ground state for temperatures ranging fkom 50 K to 140 K. Above

140 K, lasing occurs at the ground states transition of the QDs up to room temperature.

At low ternperatures, the Iasing threshold currents are found to be more

temperature insensitive than for two-dimensional quantum well (QW) lasers. At higher

ternperatures, the threshold current are governed mainly by the depth of the separate

confinement region. For samples with multiple QD layes displaying vertical self-

assembling, a broadening of the stimulated emission energy linewidth is observed.

A Bruno

Statement of Originality

Except where otherwise stated, the results presented in this thesis were obtained

by the author d u ~ g the period of her M.Sc. research project under the supervision of Dr

S. Charbonneau and in strong collaboration with Dr S. Fafard. They are to the best of her

knowledge original. These include:

1. Electroluminescence study of InAhWAlGaAs QD lasers as a function of injection

current and temperature.

2. Photovoltage and photoluminescence study of InA1AdAlGaAs QD laser structures at

T=77 and300 K

3. Threshold current density and cwent-voltage characterization of InALAdAlGaAs QD

lasers.

4. Laser structure waveguide analysis and confinement factor numencal calculations

including figure 2.8.

The TEM micrograph of figure 3.3a was produced by J. McCaffkey and figures

3.3b and 3 . 3 ~ were provided by Dr. E.M. Griswold The electroluminescence spectca of

figure 4.2 were acquired by S. Raymond and the spectra in figure 4.12 were obtained in

collaboration with J. Arlett Samples la-c and III were grown at the hstitute for

Microstmctural Sciences, National Research Council by h. S. Fafard and samples Ira-6

were designed at NRC but were grown at Norte1 Technologies by Dr. A.J. SpringThorpe.

Samples were laser processed by Dr. Y. Feng.

The above work has led to the followin~ papers:

S. Fafxd, K. Hinzer, S. Raymond, M. Dion, J. McCafEey, Y. Fens and S. Charbonneau, Red-emitting semiconductor quantum dot lasers, Science. 274, 1350 (1996).

S. Fafard., K. Rinzer, A.J. SpringThorpe, Y. Feng, J. McCafEey, S. Charbonneau, Temperature effects in semiconductor quantum dot lasers, Mat. Sci. & Eng. B 51, 114 (1998).

K. Hinzer, S. F a f d A.J. SpringThorpe, J. Arlett, E.M. Griswold, Y. Feng, Room - temperature operation of AUnAs/AlGaAs quantum dot lasers, Physica E 2,729 (1998).

F. Yang, G.C. Aers, K. Hinzer, Y. Feng, S. Fafiid, S. Charbonneau, E.M. Griswold, A.J. SpringThorpe, Visible quantum dots under reverse bias, submitted to SPIE Proc. June 1998.

Portions of the results in this thesis were presented in the following conferences:

K. Hinzer, S. Fafard, L McCaffrey, S. Raymond, Y. Feng, M. Dion, S. Charbonneau (August 1997) Optical properties of InAlAs quanium dot lasers, oral presentation at the Eighth Canadian semiconductor technology conference, Ottawa, Canada.

K. Hinzer, S. Fafard, J. McCaflkey, S. Raymond, Y. Feng, M. Dion, S. Charbonneau (Jdy 1997) S timulated emission in red-emitting semiconductor quantum dot heterostnictures, poster at the Eigh th international con ference on modu Iated semicoductor structures, Santa-Barbara, United-S tates.

K. Hinzer, Optical properties of InAlAs quantum dot lasers, presented as a tak at the 1997 Fdl OCIP graduate students seminar at Carleton University

Contributions not directIy related to this thesis:

J* Arletf F. Yang, K. Hinzer, S. Fafard, Y. Feng, S. Charbonneau, R Leon, Temperature independent Iifetime in lnAlAs quantum dots, J. Vac. Sci. Technol. B 16,578 (1998).

Acknowledgements

1 would like to thank my dynamic and supportive supervisor Sylvain

Charbonneau for allowing me to work in a laboratory with state-of-the-art equipment, for

his guidance al1 dong the project, and for his unfailhg enthusiasm. 1 wouid like to thank

Simon Fafard for the chance to work on such an intereshg project, the tremendous help

in the lab, the many discussions and also for designing and growing the simples.

1 am indebted to Sylvain Raymond for previous characterization done on this

quantum dot system and to Jesska Arlett, NRC-siammer student, for assistance in

measurements over the sulll~ller. 1 have received ongoing support fbrn Yan Feng,

Michel Dion and the entire IMS-Microfabrication group in laser processing, and TEM

micrographs essential for sample characterization fkom John McCafnrey. 1 am also

grateful to André Delage for his help on performing waveguide analysis.

During the long period the IMS MBE was offline, 1 benefited fiom Tony

SpringThorpeYs sample growth and Ellen Griswold's TEM micrographs, who are both

fiom Nortei.

Finally, 1 wodd like to thank Bruno for his immense support and both of our

families for their encouragement over the last two years.

Table of Contents

. . ................................ ..................................................*. Abstract ,. tl ..................................................................... Statement of originality iv

Achowledgements .......................... .. .. .. ................................... vi . . Table of contents .......................... .. ................................................ vu

............................................. .............................. List of figures ... ix List of tables .................................................................................. xi

. . ......................................................................... List of abbreviations xu

................................................................... Chapter 1 Introduction 1

Chapter 2 .......................................................................... Theory 5

Growth rnethod and basic optical properties of QDs ...................... 5 Energy levels d density of states for idealized quantum weIls

............................................................... and quantum dots 12 ............................. Energy levels in a lem shaped quantum dot .... 16

........................................... Interband transition selection d e s 20 Heterostructure lasers ................................ .. .. .. .................

2.5.1 Stirndated emission ...................... .. .......................... 2.5.2 Op tical waveguiding .................................................. 2.5.3 Laser characterization ................................................

Chapter 3 Experimental methods ...................................................... 38

.............................................. 3.1 Sample growth and preparation 38 ........................................................... 3.2 Electroluminescence 46

3 -3 Photovoltage and photoluminescence ................... .... ............ 49

...................................................... Chapter 4 Results and discussion 52

vii

........................................................... 4.1 Electroluminescence 52 ....................... 4.1.1 Spontaneous emission nom quantum dots 53

......................... 4.1.2 Stimulated ernission from quantum dots 56 ............................................................ 4.2 Photoluminescence 64

.................................................................... 4.3 Photovoltzge 66 ............................................... 4.4 Laser operating characteristics 67

.................... .........-... 4.5 Effects of the confinement potentid ... 70 ............................................... 4.5.1 Electro1iiminescence 71

4.5.2 QD and control QW laser characterîstïcs ....................... 76 ..................................................... 4.6 Multi-layer QD structures 81

Chapter 5 Conclusions ..................................... ... .................... 85

.................................................................................... References 88

List of Figures

Figure Page

Schematic representation of the three possible growth mechanism of thin epitaxial films.

Low temperature PL spectra obtained with an InAlAsAlGaAs QD sample probing a large ensemble of dots and N-dots.

PL spectra at T = 5 K with InGaAdGaAs QDs displaying level filluig.

Density of states for particles confined in two and zero dimensions.

Cross section view of an ideal lem-shaped quantum dot.

Schematic view of the geometry and band diagram of a heterostructure laser diode based on self-assembled QDs.

N&cd example of threshold current for lasers of different dimensionalities.

Index of refiaction as a function of the Iaser structure cross-section and eleciric field intençity in a QD laser cavity.

Cross-sectional view of the QD laser structure.

Schematic energy-band diagrams.

TEM cross-section view of the active region of samples Ia, Ila and m.

Experimental set-up for electroluminescence and photoluminescence.

Experimental set-up used for photovoltage.

EL of sample la for very low bias at T= 77 K.

Low-temperature (4.2 K) EL spectra on sample la gated with an opaque elecîrode having an opening of a few square micrometers.

EL and multimode lasing spectnun at 77 K of sample la for fonvard bises.

Spontaneous and stimulated emission spe- of a - 1 mm wide by - 1 mm long piece of sample k at 5 JS. 61 EL spectra of sample Ib at 5 K. 63

EL spectm of sample Ib at 80 K. 64

PL spectra of sample la at 77 K. 65

PV measurernents at 77 K of sample la and sample Ic. 67

Lasing properties of sample Ia at 5 K as a function of the injection current for forward-bias pulses. 69

Temperature dependence of the threshold current density for sample la. 70

Spectral output at 5 K of sample na. 72

Sample Ila threshold stimdated emission for temperatures between 70 and 100 K, 73

Room temperature spectral output of sample IIu. 74

Sketch of the temperature effects in one specific QD. 75

Temperature dependence of the threshold current density for samples la and IIa. 76

Comparison between the extemal elecîrical to optical efficiency measured with samples Ila and III at 77 K.

Laser output at T = 77 K of sample Ilb.

Temperature dependence of the threshold current density for samples lla and 1Tb.

List of Tables

Table Page

3.1 Material composition of the various lasers studied. 40

3.2 Bandgaps and conduction band offsets at room temperature in eV. 42

3.3 Estimated QD dimensions obtained fiom cross-sectional TEM aspect ratio measurements. 45

DOS

EL

F m

L C

Jrh

M.E3E

ML

PL

PV

QD

QW

SIMS

TEM

WL

List of Abbreviations

D&ty of *tes

Electtoltiminescence

Full width at haLf maximum

Excitation intensity

Threshold current density

Molecdar beam epitaxy

Monolayer

Photoluminescence

Photovdtage

Quantum dot

Quantum well

Secondary ion mass spectroscopy

Transmission electron microscopy

Wetting layer

Chapter 1

INTRODUCTION

The introduction of heterostructrues in 1970 [1] marked the beginning of

quantum confinement in semiconductor lasers. The simplest example of a

heterostructure is obtained when layers of semiconductors with larger bandgap energies

surround a lower bandgap material. Either one of these layers can be doped with donor

or acceptor impurities, with the possibility of forming a p-n junction at one of the hetero-

interfaces. Basic understanding of such low-dimensional systems and applicability of

heterostructure concepts has become possible in recent years due to improvement of

growth techniques such as molecdar beam epitaxy W E ) .

The energy band in a semiconductor crystal reçults f?om the periodic structure of

an infinite lattice. When the crystai thickness is finite and thin enough to be comparable

with the de Broglie wavelength of an electron in a semiconductor (= 10 nm), one obtains

a structure confined in one-dimension known as a quantum well (QW). Perpendicdar to

the well plane (z-direction), electrons are confined by the potential well created by the

double heterostructure, resulting in a structure having discrete quantized energy levels.

Along the well plane (x-y plane), the crystal is assumed infinite. The density of states of

carriers in the QW is modified firom the conventional Etdependence for buik materials

to a step-like dependence [2]. Such lower dimensional structures can be used as the

active region of semiconductor lasers. It was first predicted theoretically, and

subsequently conkned experimentally, that this reduction in dimensionality of the

active region results in superior Iasing characteristics includùig lower threshold currents

and improved temperature stability. Today, semiconductor laser diodes based on QWs

are the key components in optoelectronic and photonic uitegrated circuits, and play an

essential role in the expanding information technology and communication industry [3].

They are used in a wide range of applications fiom optical fiber cornmuIllcation systems

to barcode scanning, including optical storage, image recording. and displays for

entertainment and instrumentation. These devices are capable of hi& powers and

efficiencies at a variety of wavelengths in the visible and the innared.

By increasing the confinement of c&s in the other directions (x and y),

systems with lower dimensions c m be obtained: quantum wires (QWRs) and quantum

dots (QDs). in which carrier motion is conhed to one and zero dimension respectively.

Because of the 3D-quantum confinement, the energy spectra of electrons and holes in

QDs can be considered discrete. This delta-fùnction-like density of states of QD systems

leads to an effective absence of carrier thermal distribution, independent of temperature,

in contrast to QW and bulk structures. The main expected advantage in Uitroducing QDs

as the active medium of a semiconductor laser over conventional QW lasers is a lowering

in threshold current density due to the discrete nature of the density of states [4]. Other

predicted advantages include: higher modulation speed, reduced temperature sensitivity,

higher optical gain, and wider spectral gain profiles [4-71. For these reasons, structures

with QDs as active regions have generated much interest recently as a new class of

artificially stnictured materials having discrete atomic-like states with tunable energies,

through composition and size variations, that are ideal for use in laser structures.

Pnor to 1994, only one research group had reported light emission fiom quantum

dots through current injection [8], using standard lithographie techniques for the

fabrication of QDs. An important advance in the fabrication of zero dimensional

structures exploits one of the naturd consequences in growth modes for dissimilar

mataials. QDs grown in this manner make use of a mature epitaxy growth process

without requiring any additional processing. As well, their ability to emit at a range of

wavelengths by simpIy using the various well understood and characterized III-V alloy

systems, make them perfect for immediate integration into practical devices. The

samples characterized in this study were grown using this fzbbrication technique.

This thesis focuses on the optical properties of self-assembled quantum dots

grown in the InAlAdAlGaAs alloy system, and more specifically on their use as active

material in QD lasers. QDs made of this material system have emission wavelengths

correspondhg to the red (650-730 nm) portion of the spectnim [9] allowhg for possible

applications in higher-density optical storage, or in display and illumination. Chaptes 2

begins with a review of the basic properties of QDs and goes on to describe gain and

waveguide analysis in heterostnicture lasers. Chapter 3 includes a description of the

samples, laser fabrication, optical measurement techniques, and apparatus. Resdts

obtained fiom rneasurements of &-,AI,&/AlGaAs QD lasers are presented and

discussed in chapter 4, beginning with the evidence for stimulated emission nom QDs.

The effect of potential barrier height of the connning layers on laser characteristics is

analyzed, and the properties of lasers grown with multiple QD layers are presented.

Finally, a summary of the resdts and cornparison with other systems appears in the

conc tusion.

Chapter 2

THEORY

This chapter is intended to give background information on the system studied

and is divided into three sections; the nrst describes growth methods and basic optical

properties of QDs while the second evaluates the energy levels and density of states for

idealized heterostnictures followed by the equations used to calculate the energy levels of

a more redistic system: the lem shaped quantum dot. The chapter concludes with a

discussion of gain and threshold curent density in heterostructures of different

dimensionality as well as an analysis of light propagation in slab waveguides.

2.1 Growth method and basic optical properties of QDs

Zero-dimensional semiconductor structures may be obtained through epitaxial

growth techniques. Two principal methods cm be distinguished: (1) the growth of two-

dimensional layered structures (QWs) followed by successive etching procedures that

lowers the dimension; and (2) epitaxial techniques u t i l k g self-organized island

formation in highly mismatched (- 4%) epilayer/substrate growth systems.

The first method for nanofab~cation of semiconductor materials uses lithographie

and etching techniques to produce dots with diameters of -25 nm [IO-141. Other

fabrication techniques used in production of QDs include intermixing where a focussed

ion beam having a diameter of 50 nm was used to mod@ the lateral bandgap profile

[15], gate modulation of patîerned connnllig layer [16] and overgrowth on vicinal

surfaces [17]. It has been shown that the etchhg techniques required in the fabrication of

QDs through pattern transfer ont0 semiconductors introduces additional damage forming

a depletion layer at the surface of the pattemed device, and thus affects the electronic

properties of the rnaterials. This damage manifests itself on a microscopie level in the

form of nonradiative defects such a dislocations and vacancies [18]. In the case of gate

modulation devices and intermixing techniques, reduced carrier confinement are

obtained, naking the observation of quantum effects possible only at very low

temperatures. Dots may also be obtained by growth of nanocrystals in glas mairices,

and in organic materials and related matrices [19]. Electrical injection of carriers is

difficult in these systems however, making them less than ideal candidates for device

applications.

The second class of "nanofabrication" technique, which relies on the formation of

lower dimensional structures during epitaxial growth, has recentiy attracted a lot of

interest. Strain induced self-assembled growth leads to the formation of small dots

(about 10 - 30 n m diameter) having good size uniformity, and a hîgh density (between

108 to 10" dots/cm2). In the past five years, dots have been grown in a variety of III-V

semiconductor systems including InAdGaAs [20], InAlAdAlGaAs 191, and MslInP

[21], in II-IV materials like CdSe/GaAs [22] and in the indirect bandgap group-N

system SiGe/Si [23]. Since the fabrication of dots is intrinsic to the growth method used,

this technique is attractive for device applications mostly through its compatibility with

commercial growth syçtems as well as the availability of ultra pure elements needed for

growth. Control of the QD energy levels is possible by varying the growth conditions.

For example, S.-2. Chang, T.-C. Chmg, and S.-C. Li have observed that for systerns

with low lattice mismatch (1-2 %), the QD density is hi& and the QD sizes are small; for

larger lattice mismatch (> 2 %), the QD density is lower and the QD sizes are larger [24].

The growth temperature is another important factor in determining both the ground state

energy level and the intersublevel spacing of the QDs [25]. The QDs used in this study

were obtained through spontaneous island formation.

Layer by layer Volmer-Weber Stranski-Krastanow

Figure 2.1 Schematic representation of the three possibIe growth mechanism of thin epitaxial films.

There are k e e known modes of heteroepitaxial growth [23]: Frank-van der

Merve mechanism or layer-by-layer growth [26], Stranski-Krastanow mechanism or

layer-by-layer growth followed by 3D island formation [27], and Volmer-Weber

mechanism or island growth [28] (figure 2.1). The selection of one growth mode over

another depends on the epitaxial layer and the substrate on which it is to be grown. h

fact it was s h o w that, owing to the difference in nature and strength of the chemicd

bonds, and the lattice parameters, the three growth modes codd be covered [29].

Because of these fundamental parameters (bond strength and lattice parameters), the

chernical potential of the overgrowth differs nom that of an infinitely large crystd.

Across the interface, the atoms of the deposit can be bound more loosely (or tightly) to

the substrate atoms than to the atoms of the same crystal. Consequently, the chernical

potential of the fist layers of the deposit could be hi* (or lower) than the chernicd

potential of the infinitely large deposit crystal. The Volmer-Weber growth mode occurs

when the interfacial bonding is weaker than the bonding in the deposit itself, that is, the

achtoms will have a tendency to form islands on the surface to minimize the interface

area In systerns having strong interfacial bonduig, layer by layer growth occurs; the

atoms '%ety' the entire surface. At this poinf the Iattice misfit plays a prominent d e in

determinhg the growth mode. The larger the misfit, the greater the tendency towards

island growth, and vice-versa. Generdly, layer-by-layer growth occurs if the misfit is

smd. If the misfit is substantial, coherently stcained islands grow on top of the wetthg

layer (WL) until they reach the dislocation-formation critical thickness. This is h o w n as

the Stranski-Krastanow growth mode. The size and shape dispersion of these islands is

very small at the omet of island growth. If the growth is allowed to proceed above the

critical thickness with the same lattice mismatched material, generation of dislocations at

the interface between the layer and the substrate will occur, producing main relaxation.

Once fomed, these incoherent, strain-relaxed islands, continue to grow with littk

restriction until a complete two-dimensional film has been developed If, on the other

han& before reaching the critical thickness, the distocation-fiee dots are capped with a

materid having the same lattice constant as the substrate, the growth proceeds epitaxially

without introduction of dislocations. The QDs are then sandwiched between two similar

epilayers.

The optical excitation of self-assembled QD systems yields bnght luminescence

and generally reveds a Gaussian line shape distribution (figure 2.2a). In the case where

nonresonant excitation is use& photoluminescence (PL) data display smooth and

structureless spectra. Typically for such PL experiments, the spot size is of the order of

100 pm diameter, and therefore for characteristic dot densities of 200 ~ r n - ~ , a large

number of QDs are probed (- 106 dots). The PL data therefore reflects the statisticai

distribution of the ground state energy levels of the individual dots that &ses fcom the

slightly different zero dimensional connning potentials. Since the QDs have a deep

confining potential and a relatively small height-to-diameter ratio, this distribution

should arise rnainly fkom the additional atorns dong the growth direction. Other

parameters, such as small variations in the diameter, in the alloy composition, or in

partial (defect-fiee) strain relaxation, can also contribute to the observed inhomogeneous

broadeniug in the emission specirum.

A smdler number of QDs can be probed through the use of mesas, etched fkom

the QD structure, of different sizes [9] or simply by performing micro-PL, where the

probing laser spot size is reduced to the difhction limit (- 1 p). Figure 2.2b shows the

results obtained on mesas of different sizes (3, 7 and 13 @) obtained fkom the same

sample as in figure 2.2% having a dot density estimated at 200 per pm2 (fiorn TEM plane

view measurements). The correspondhg number of dots probed is estimated at N - 600, 1400, and 2500 dots respectively. For the mal1 mesas containhg only a few hundred

dots, the PL spectnim displays distinct, very narrow lines (full with at half maximum

(FWTEM) - 100 peV). As the d e r of dots probed increases, the spectra becorne smooth, as expected, by considering the statistics of large number of added lines. The

appearance of the sharp spectral Enes is an indication of the zero-dimensional nature of

the density of states (DOS). As the temperature of the system is increased, the sharp -

spectral features observed in the small mesa PL spectra do not broaden [3 11.

-60 -40 -20 O 20 40 60 Energy from the peak (rneV)

Figure 2.2 (a) Low-temperature PL spectra obrained with an InALAdAIGaAs QD sarnple, probing a large ensemble (-106) of 17-nm diameter dots under the excitation spot, and a Gaussian distribution f i t (b) PL of N-dot ensembles delineated with p-sue mesas, displaying statistical fluctuations. Two scans are shown for each mesa to evaluate the reproducibility of the sharp feanires. The peak position for the InAlAdAlGaAs QD ensembles is A = 660 nm [9].

This temperature-independent emission linewidth was predicted theoretically and is

simply a consequence of the Gfunction like density of states due to the zero-dimensional

nature of the dots. Exciton lifetime measurements done on these sharp spectral features

were shown to be constant with temperature [31, 321 up to the onset of thermionic

emission; a fbrther evidence of the zero-dimensional nature of these self-assembled dots.

The atomic-like discrete energy spectrum of each QD state c m easily lead to a

state-filhg effect at higher optical excitation, due to the exclusion prhciple when only a

few carriers can populate the lower states. In fact, in recent publications it was

emphasized that only two electrons c m occupy the ground state level of a dot (spin up

and spin down), four eIeclrons in the f is t excited state (n = 2) and so on U3]. This

causes hindered inter-sublevel dynamics and observation of excited state interband

transitions as the excitation intensity is increased. State-filling will show clear saturation

effects as well. At low excitation intensities, only the (inhomogeneously broadened)

ground state levels are generally observed because of the fast inter-sublevel relaxation

process taking place. As the intensity is increased, a progressive saturation of the lower

energy transitions is combined with the emergence of new emission peaks originating

fiom the excited state interband radiative transitions. These effects are observed as the

inter-sublevel carrier relaxation towards the lower levels is slowed due to the reduced

number of available final states 134-361. An example of state-filling effect, where the

intersublevel spacing is larger than the inhomogeneous broadening, is depicted in figure

2.3 for the InGaAs/GaAs system [37]. QDs having larger dimensions or deeper

potentials are expected to have more bound states.

Energy (eV) Figure 2.3 PL spectra obtained at T = 5 K with different excitation intensities (IA with h&a,&dGaAs QD's, 36.5 nm in diameter, displaying strong Ievel filling and emission fiom the excited states and saturation of the gound states with increasing excitation intensities. 1, - 10 ~ f c m ' C3 71

2.2 Energy levels and density of states for ideaked quantum weils and quantum dots

The advantages of using low-dimensional structures arise mainly fiom the changes in

the density of states as discussed previously [4]. The density of states for electrons and

holes in basic systems are calculated using Schrodinger's equation [38, 391:

where m* is the particle effective mass and E represents the energy of the p d c l e fiom

the band edge. The hard wall approximation for the potential is use& Le. the potential V

is zero inside the structure and the barriers are infinite. In the case of a cubic potential,

separation of variables is applied to solve equation 2-1. For fiee-particles, the

wavefunctions have the form of a travelling plane wave

yv =e*v% (2-2)

where kv is the particle wavevector with the allowed values k, = x n , / L and

n, = f 1, + 2,. .. In Cartesian coordinates, v can be replaced by x, y or z and L represents

a macroscopic length. In the case of particles c o f i e d to a microscopic dimension, the

particle energy levels are quantized and the wavefunction becomes

where IV is a microscopic length and k,, = rrn& with n, = 42, ... The total energy is

given by:

For a two-dimensional quantum well, the motion along the growth direction (2) is

quantized, so the allowed energies in the direct ion are

The particle wavefunction Y is confined to the well width Z=. The density of states up to

and including those of energy E is equal to:

where B(E) is the unit step Eunction [B(E 2 0) = 1 and RE) c 0) = O] and n= is the -

subband quantum number. Therefore the two-dimensional density of states has a

çtaircase shape, as shown in figure 2.4a.

For quantum dots, quantization occurs in a l l three directions and the allowed

energies are

with a zero-dimensional density of -tes expressed as:

where n , n, and R are the quantum numbers for the allowed energies in the respective

directions. This density of M e s has discrete values as can be observed in figure 2.4b.

(a) Quantum well

(b) Quantum dot

Figure 2.4 Density of states for particles confined in (a) two dimensions (the bulk density of States is s h o w for comparison), and in (b) zero dimensions.

As the dimensionality of the structure is decreased, the density of states becomes

increasingly discontinuous and the onset of energy levels shifts towards higher values.

These effects are independent of the shape of the structure studied, as long as comparison

is done between mctures of macroscopic and microscopie dimensions.

In the case of self-assembled quantum dots, the density of states calculation must

take additional factors into account, the most important being the size/composition

inhomogeneity of the dot population. The allowed carrier energy level positions and

intersublevel spacings in the QDs will then Vary slightly for dots of different

size/composition. This will result in a state distrïbution having a certain width: the larger

the population inhomogeneity, the wider the distribution.

2.3 Energy levels in a lem shaped quantum dot

In the InA1As/AlGaAs system, the quantum dots can be modeled as lem-shaped

(see figure 3.3). Such modeling has been done previously 133,401 with numerical results

for QDs in the InGzAs/GaAs system. The disks are on top of a narrow quantum well, -

also lmown as the wetting layer, of thichess t, and can be modeled as part of a sphere

of k e d height 1, and base radius p, as shown in figure 2.5. The bonom of the

conduction band of the W L and QD material is below the bottom of the conduction band

of the surrounding material. The carriers, c o f i e d to a thin QW, are M e r localized in

D x-y plane

Figure 2.5 Cross section view of an ideat lem-shaped quantum dot

area of the dot due to the effectively increased thickaess of the layer at these points. The

dots have a base diameter in the nanometer range, so that lateral confinement is not

negiigible.

If an electron-hole pair is trapped in a lens-shaped dot, the effective Harniltoiiian

c m be expressed as:

e2 ph2 H z - +-- e2 2me 2m, &[r=-rh[ + v(rJ + v(rA 9

where the subscripts e and h stand for electron and hole, V(rJ and V(rJ are the carrier

confining potentials due to the dot shape and the middle term is the Coulomb interaction

inside the dot. For dots of small dimensions in the so-called strong confinement range (R

cc a,, where R is the electron-hole distance and a, is the excitonic Bohr radius),

Coulomb interaction effects are neglected [41]. The problem therefore simplifies to the

one-particle effective-mass Schr6dinger equation (equation 2-1) for both electrons and

holes. The adiabatic approximation is used to mode1 the contùiing potential V(r) for the

dot. This method states that the potential a particle feels, when moving in the x-y plane,

is given at each point by the ground state energy of a quantum well of equivalent

thichess Z(,). The connning potential is zero inside the dot and wening layer, but finite

outside. Equation 2.1 can be transformed into an equivalent system of equations [33]:

fi2 â Z q ( x ) -- * 6k2

+ vxfl(DX(x) = EXax ( x ) 2%

(2- 1 Oc)

E=E,+E,+E, and (2-Lod)

v?' is the potential of an InA1AdAlGaAs quantum well of width Io + t , ,

vX' = E~' (~(x)) - E~~ (lo + t,) and Y'@ = E Q ~ ( ~ ( ~ ) ) - E~~ (2, +t, ) are the effective

potentials obtained fiom the adiabatic approximation. rn: (2) is replaced by the ALInAs

effective mass (m:) for O < Izl c 1, +t,, and by the barrier layer effective mass (mi)

otherwise.

The energy levels of a quantum well of thclmess 1 can be obtained numerically

fiom 1421:

The resulting spectnim consists only of discrete bond -te energies. The &eus are

spaced evenly (intershell spacing of the order of tens of meV), and the intershell spacing

demeases with increasing dot size. The number of bound states increases with increasing

barrier height As stated in section 2.1, the £ïrst bound state is filled up with two

particles; the second bound state is filled after four particles and so on. This mode1 does

not take the effects of strain into account; more accurate models have been developed for

lem-shaped dots [333] and for pyramidal dots [43].

In practice, however, the quantum dots obtained through the Stransla-Krastanow

growth mode have potential barriers with f i t e heights, that is, at elevated temperatures

carriers cm escape the confïned region by thermionic emission into the barrier material

1441. This important carrier-loss process is especidy significant in structures with

shallow barriers 1451. The carrier distribution between the active region (QD) and the

connning layers (barrier and WL) is controlled by carrier thermalizatiodcaptuce

processes in the QD and the escape processes fkom QD to WL or barrier through

therrnionic emission. The probability per unit time for a carrier to absorb phonons and

be emitted above the barrier is greatly enhanced at high temperatures due to a large

phonon population in the lattice. Consequently, quenching of the emitted light intemit/

is observed at higher temperatures according to an exponentid law of the form

where c and a are adjustable parameters, k,T is the thermal energy, and EA is the

activation energy which corresponds to the minimal energy necessary to promote carriers

to unbound energy levels. The onset of thermionic emission depends on the values of a

and EA.

2.4 Interband transition selection rules

Due to their discrete energy states, the transitions between the electron and hote

levels in QDs are analogous to those between the discrete levels of individual atoms.

The band-to-band transition probability per unit time is given b y Fermi's golden d e . In

the case of the creation of a photon [46] :

where e is the light polarization vector ande is the momentum operator. The sum is over

al1 the levels in the conduction and valence bands (initial states 1 i) and final states I f ) ).

Ei and Ef represent the energies of the initial and final states, (f (es @li) is the optical

ma& element expressing the coupling between the initial and final states with the light

polarization, and the tenn preceding the s u . represents a constant of the system.

Conservation of momentum and energy accompany emission and absorption of photons.

The reduced density of -tes observed in low-dimensional systems (compared to

the usual bulk probability transitions) is htroduced in the SUIILrnation over initial and

final states to account for dixnensionality in the wavefunctions and the joint density of

states. The electron and hole wavefunctions Y,,(r) in low-dimensional systems are a

product of the envelope fûnction X(r) and the appropriate Bloch function un,, (r) at the

r point, Y (r) o x (r) un,, (r) . The rnatrix element in (2- 13) can be factored into the

integral over the unit ceIl of the fast varyhg part of the wavehction (the Bloch

function) and a sum at the ceIl centers R, of the slowly varying functions (the envelope

hction).

The optical ma& element for transitions that involve an electron £iom a

conduction band and a hole fiom a valence band is:

where e and h represent electrons and holes and the integral is over unit cells. The

electron and hole wave vectors are designated as k, and 16. nie exponential factors give -

a nul1 contribution d e s s = h, which is the vertical transition nile since light has

negligible momentum. When factoring the electric-dipole matrix element in equation

(2-13), the change in parity of electric-dipole transitions appears in the Bloch integral

matrk element; this is just the same as in bullc systems.

The other selection d e s have MO origins: the overlap integral between envelope

hc t ions selects the quantum numbers of the initial and final level and the atomic-like

dipole matrix element imposes the selection niles on polarkation of the light wave. The

atomic-like part of the Bloch wavefunction is similar for al1 III-V materials and the

polarization selection d e s are not dimensionality dependent.

The matrix elements for the envelope functions are integrals over their product

with no potanZation dependence. If the electron and hole quantum dot potentials are

symmetnc, the envelope functions could be symmetnc or antisymmetric and their matrix

elements will vanish unless both have the same parity. Ifthe potential in both conduction

and valence bands can be modeled as a quantum box with infinite potential walls, then

the two sets of envelope fiinctions are identical and o d y transitions between levels with

the same index are allowed, this is the "An = n - nt = 0" d e , where rn is a valence-band

state and n is a conduction-band state. In the case of lens-shaped dots, quannim dot

wavefunctions have to be used, which for the £îrst few leveis can be approhated by in-

plane harmonic functions [40]. For this case, the d e changes to "Anr = n, - m, = O"

and "Any = n,, - rn, = û". Also, the envelope functions are not exactly orthogonal since

the effective depth of the confinhg potential is different for electrons and holes. This can

lead to observations of transitions between n # rn states. These transitions will have weak

intensities, and in order to conserve parity, n - m = odd hteger will o d y appear in the -

case of highly asymmetric potentials.

2.5 Heterostructure lasers

Electrically injected carriers in a p-n jmction can recombine both radiatively and

nonradiatively. The radiation originating from the recombination of carriers can interact

with valence electrons and be re-absorbed, or interact with electrons in the conduction

band to stimulate an identical photon. When the injected carrier concentration becomes

large enough, the stimulated emission can exceed the absorption so that optical gain

occurs. In order to sustain stimulated emission, a portion of the radiation mut be

reflected back to the laser medium. This way, the power gain due to amplification is at

least equal to the total losses, including that of the oscillator output.

In the present work, separate confinement heterostructures are used to provide

localized gain. The uiner jmctions or heterojunctions are used for carrier confinement

and the outer heterojunctions are used for optical confinement. In Fabry-Perot laser

cavities, cleaved facets act as a pair of reflectoa and thus f o m the resonant cavity. A

stripe electrode is used in order to restrict the injected current to a given width (figure

2.6).

The theory developed by Lasher and Stern [45] to analyze the interaction between

electrons and light in semiconductor lasers is presented in section 2.5.1. Calculabons -

based on this model performed by Arakawa and Sakaki [4], and by Asryan and Suris [48]

for QD and QW lasers are summarized In section 2.5.2, the multiple waveguide model

is explained as well n d c a l analysis results of the samples studied are presented

Figure 2.6 Schematics of (a) the geornetry and @) the diagram of conduction band (CB) and valence band (VB) of a heterostmcture laser diode based on self-assembled quantum dots. ïhe electrons (-) and holes (+) are iojected in the active region with a forward bias voltage (V) and current (4.

The threshold current density of a semiconductor laser c m be obrained fkom the

recombination rate equations [47]. Electrom (holes) cascade down (up) the quantum dot

potential by p honon emission a d o r thermalize by electron-electron @oie-hole)

interaction. Considering electrons in the Limit of strong electron-electron interaction, i.e.

under strong canier injection such as for Iasing conditions, a Fermi-Dirac distribution is

established:

*

where E is the energy measured from the conduction band edge E, F, is the electron

quasi-Fermi level measured nom the edge of the conduction band, k is Boltzmann's

constant, and T is the temperature. The holes have a similar distribution function,f,:

where E is the photon energy.

With the densities of states obtained in section 2.2, and assurning An = O

transitions, one can obtain the net rate of stimulated emission T$,(E), also called the gain

coefficient, and the rate of spontaneous emission, r,J&). Using the 'ho k-selection d e "

mode1 of Lasher and Stem [48], one can obtain

where (i) stands for OD in quantum dots and 2D in quantum wells, B" is a constant

representing the probability of dipole barsitions, E, is the energy gap, c is the velocity of

Light, and n, is the rehctive index. The electron quasi-Fermi level is adjusted in such a

way that the maximum gain g"'(E) satisfies the threshold condition, Le., &'(E-) is equal

to the total optical loss in the laser cavity, which we assume to be independent of '

temperature. Because of the effects of the density of states, the spectral gain profile will

be narrower for low-dimensiond structures. The gain spectnim becomes discrete in the

case of quantum dot lasers.

The rate @;)of the total spontaneous emission is calculated by the energy integral

of the spontaneous emission rate

The rate equations for electron density, n, and number of photons, N,, in the Mh

lasing mode may be written as [49]:

d t e d ' 7 ' L ~ w ~ ~ @ ( & )

where d is the width of the active region, 7 is the quantum efficiency, Ld and W, are the

length and width of the device, s, is the photon lifetime in the lasing mode, and M' is the

number of sponraneous modes. The number of modes per unit energy per unit volume is

given by:

For simplicity one lasing mode is assumed (rn = 1) and M' is very large so the second

term of equation (2-21) is neglected. Under steady state condition, at the lasing

threshold, the two rate equations (2-20) and (2-21) become:

These two equations contain the two unknowns, and R:;), which can ody be

solved when the two quasi-Fermi levels, F, and F, are given. In general, the threshold

curent density is calculated numerically, but analytical expressions can be obtained for

quantum well and quantum dot lasers as given by [4]:

a ed m, - - --Po B ( ~ D ) ~ T i.( kr ] (at high temperature) (2-25) 7rh21z P O X ~ L

where V = IJ,, 1; , .=[

& +(D-l)'"(l+~) t + C - C D

hole effective masses, p, is the hole concentration in the laser active region, and d7 is the

loss coefficient due to difiaction, fkee carrier absorption, etc. Equations (2-25) and (2-

26) indicate that the threshold current density of a quantum well laser is proportional to

~ln(~/constant) near room temperature, whereas J, of a quantum dot laser is

independent of temperature.

Numericd calculations of J, from the model described above have been

performed for the GaAdAlGaAs system [4] assuming that electrons populate o d y the

ground state subband/sublevels, which is valid when !, 2' Z= are sufncientiy small. The

results for T near room temperature are summarized in figure 2.7. They clearly show

that the temperature dependence of J,, changes drastically with the degree of confinement

of the can5er motion. In order to compare the temperature dependence of J, for these

devices, we express the r e d t s in terms of the conventional expression that is used to

characterize semiconductor laser performance:

4 = J& (T, ) eV (y). A high value of T, indicates relative temperature insensitivity for the laser device.

Typical characteristic temperature values are T, = 120 - 160 K for a GaAdAIGaAs

double heterostructure laser diode operating at room temperature [50]. T, values

obtained theoretically through this model for conventional double heterostnictures,

quantum well, quantum wire and quantum dot lasers are 104, 285, 48 1 OC, and m,

respectively.

The reason for such a dramatic increase in T, can be understood as follows: for a

conventional double heterostnicture laser, the intrinsic temperature dependence of J ,

(which is not related to a leakage over the b h e r and Auger processes) is ascrïbed to the

thermal spreading of the injected carriers over a wider energy range of states, which

leads to decreases of the maximum gain g(E-) at a given injection level. Consequently,

in quantum well lasers, where the density of states of the electrons and the holes are step-

Iike, the effect of such thermal spreading is expected to be smaller than in bdk-based

lasers. In quantum dot lasers, the thermal spreading of carriers should vanish because the

density of state is ô-function-like. Hence, the temperature depeildence of J, will totaily

disappear, as long as the electron population in the higher leveIs rernains negligibly

Figure 2.7 Numerical example of threshold curent J;A caIcuiated by extending the theory put forward by Lasher and Stem [48] for (a) a double heterostmcture laser, @) quantum well laser, (c) quantum wke Iaser, and (d) a quantum box laser [4].

The structures studied in this thesis have finite-height potential barriers and, as

mentioned at the begirining of this chapter, the quantum dots have inhomogeneous

broadened energy distributions. In the theoretical analysis of gain and threshold current

of quantum dot lasers done by L.V. Asryan and R.A. Suris, these factors are taken into

account [5 11. Their analysis considers three variables: the operating temperature, the QD

size fluctuations and the conduction and valence band offsets between the QD and barrier

material.

In the case of relatively low temperatures and/or deep potential wells, the

radiative lifetimes in QDs are small compared with the characteristic times of thermal

excitation (escape) of the carriers f?om a QD (nonequiiibrium filling of QDs). Having

insufficient time to leave the QD, the carriers recombine within the dots and the

threshold current density is essentialiy temperature independent as in the mode1 desrribed

previously. The inhomogeneous broadening of the QD ensemble does not affect J,.

When the system is at relatively high temperatures and/or the structure has

shallow potential wells, equïlibrium fiIling of QDs occurs. In this case, the charactenstic

times of therrnaily excited escapes of electrons and holes korn the QDs are small

compared with the radiative lifetimes in QDs. If the inhomogeneous line broadening

(AE),,, is less than the temperature, J;, is found to be proportional to the square root of

(LE),.,. When the inhomogeneous line broadening is larger than the temperature, J,

increases lineariy with increasing (LE),,,,,.

These rnodels assume that only the fint quantized states @oth in the conduction

and valence levels) are involved in the transitions.

2.5.2 Optical waveguiding

For a laser to function, one needs an active medium for light amplification, QDs

in the case of the samples studied for this thesis, and a resonating cavity, Le. two mirrors

delimiting a cavity capable of optical mode codbement such as a waveguide. The slab

waveguide consists of a slab of hi& refkactive index material sandwiched by lcw index

material. Assume that light propagates in a guided medium dong the y-direction. The

light is confined in the z direction by the difference in refkctive indices but diverges in

the x-direction because there is no guiding structure in this direction (see figure 2.6a).

Waveguiding in the x direction arises fiom the difference in gain behileen the regions

undemeath and outside the electrodes in Fabry-Perot lasers.

The guided light propagates dong the y-direction with a sinusoida1 t h e

dependence (a, not explicit here) according to the wave equation [52]:

~ ~ ~ = k i - n : ( x , ~ , z ) ~ , (2-28)

where the symbol E in the scaiar theory represents the dominant component of the

elecbomagnetic field, k, = 216A = d c , n, is the index of refraction of the medium, and w

is the angular fkequency. When n, is pinvariant, the wave behavior can be described in

terms of modes characterized by a constant of propagation and a y-invariant mode profile

of the electric field dx,z):

The lower case letters refer to the guided modes, wlde the uppercase represents the

continuum of radiation modes that are necessary to take into account the part of the Iight

energy that is not guided in the waveguide. These modes decay very rapidly with y since

the continuous function B(v) is imaginary.

If we consider only the guided modes @-invariant Ki profile by definition), we

obtain:

V : y l + k i - n : - v = / 3 2 - V I . (2-3 O)

The symbol I is used to indicate that the derivatives include only the direction

perpendicular to y and P is the propagation constant. This simplified equaticn is used to

determine the mode pronles in conjunction with the appropriate elec~omagnetic field

boundary conditions. These solutions are obtained numerically since only simple

waveguide cases can be treated analytically [53]. In order to obtain the condition of total

internai reflection inside the waveguide, the core material must have a larger index of

refiaction than the cladding material. Eigenmodes of the system must satisQ the

equation above, both in the x and z directions. The modes have well-defked field

distributions in the transverse x and z directions (transverse modes) and propagation

constants in the y direction which are determined by the standing wave condition. The

field intensity is the density probability of photons. A simila. analysis can be done for

the magnetic field H.

Modeling of the eigenmodes for the lasers in this study was done using the

mdtilayer slab guide mode1 [54]. This technique is used when the slab waveguide

structure has many layers. The analysis of multiiayer stacks starts with the theory

explained above as well as Maxwell's equations and defines two field variables U and W

by

U=E, , W = o p H , (2-3 1)

which describe the transverse variation of the opticd field Here p represents the

permeability constant. These defuitions are chosen because U(z) and W(z) are quantities

that are continuous at the layer boudaries. From solutions of Maxwell's equations for

planar guides, we obtain the relations

u = - j w (2-32)

2 2 w ' = j ( p 2 - n , k )u, (2-33)

where the prime indicates differentiation with respect to r, and j is equal to n. Bath Cr and W obey the transverse wave equation

~ " = ( p ~ - n : k ~ ) ~ . (2-34)

U and W describe the transverse field distribution in a particula. layer of constant

refktive index n, The general solution of the wave equation in this layer is

U = A e q ( - j ~ x ) + ~ e x p ( j ~ x ) (2-35)

W = K [ ~ e x ~ ( - j ~ x ) - ~ e x ~ ( j r x ) ] , (2-3 6)

wiere the wave number K ~ S defined as

r2 =nf k2 -p2 , (2-3 7)

The constants A and 3 c m be replaced by the input values U, = U(0) and Wo = W(0) at

the input plane z = O of the layer. We obtain

A rearrangement of (2-35) - (2-39) leads to a simple matnx relation between the output

quantities U, W and the input quantities U, Wo

where the pairs (U,, Wo) and (U, W) have been M e n as vectors, and M is the

characteristic matrix of the layer. It has the form

cos (KX) 61.) sin(.x M = l

j s ) COS(KX)

Note that det M = 1.

Now consider a stack of n layers sandwiched between a substrate and a cover.

The layer thichesses are hi (labeling the layers st&g fiom the cover) and the laye

indices are ni, where i = 1 to n. The output field variables for each layer are (l. and Wp

The characteristic matrices for the layers are

cos (K, hi ) (jffc,-)sin(~~ hi j s i hi ) COS(K, hi )

where

~f =n:k2 - pz .

The corresponding field variables are related by

Using matrix multiplication, we obtaui a simple relation between the input variables U,

W, at the cover and the output variables U,, Wn at the substrate

where M is the cbcteristic ma& of the stack The product of the individual layer -

matrices gives

where m,,, ml, etc. are the matrUr element used in the analysis.

Numerical calculations were carried for the waveguide structure shown in figure

3.1. The change in index of rehction as a function of the laser structure cross section is

displayed in figure 2.8a The results demonstrate that the dominant guiding modes of the

stnicture are the first transverse eleceic and transverse magnetic modes. Figure 2.8b

displays the electric field intensity of the k t guided mode. The narrowness of the field

intensity testifies that the outer heterojmctions confine the photons well (owing to the

large change in index of rehction between the AbZGib,,As and the Aio~70G~,,,As

regions). The Iasing threshold current is iduenced by the mode confinement factor c, which is the ratio of the optical power in the active layer to the total optical power

If the structure s h o w in figure 2.8 has one stack of quantum dots (as sample Ila

in chapter 3), the confinement factor for the dots is calculated to be - 0.5 %; Le., there is a 0.5 % overlap between the optical mode and the QDs. For a laser structure having five

stacked layers of dots with 7 nm spacer layers (sample Ilb in chapter 31, the confinement

factor increases to - 2.5 %. Quantum weLI laser structures have confinement factors ranging between 2 and 10 % since weUs are usualiy thicicer than QDs [55]. Furthermore,

self-assembled QDs cover at most 50 % of the x-y plane ([32, 56, 571 and figure 3.3) -

compared with 100 % for QWs, thus redting in lower confinement factors for these

structures.

Figure 2.8 (a) Index of rehction as a function of the laser structure cross section for sarnples IIa and Ilb. (b) The doted line represents the electric field intensity of the fkst guided mode in the quantum dot laser cavity. The cladding layers are symmetric on both sides of the active region.

2.5.3 Laser characterization

This section states the equaîions used for the characterization of laser properties

presented in chapter 4.

The e l e d c d input power Pd, provided to a laser structure is measured as Pd, =

RJ2, where R, is the sample resistance and I is the current delivered to the device. This

resistance can be determined fkom a curent-voltage (1-V) plot

The device external quantum efficiency q, for stùnulated emission is defined as the ratio

of the rate of photons leaving the exit interfaces (W,) to the rate of carriers crossing the

junction [58], that is

where P is the output power fkom one facet of a laser. The factor 2 in equation (2-49) is

included to account for light exiting fiom both facets. When one includes the power

losses fkom the residual contact resistance, the above equation becomes

- 2P '7m - (2-5 O) I V , - I ~ R , '

Equation (2-27) is used to chantcterize the threshold curent as a function of temperature.

For curent values above the threshold, many emission lines may be observed in

the laser spectrum. These lines belong to the various longitudinal modes of the device,

which can be amplified simultaneously. The basic mode selection in the y-direction

(longitudinal direction) arises fkom the requirement that only an integral number rn of

half-wavelengths fits between the reflection plane. Thus

m R=2Ld n,, (2-5 1)

where L, is the device length and n, is the refiactive index. The separation AA between

these allowed modes in the y direction is the difference in the wavelengths corresponding

to rn and in + 1. DBerentiating the above equation with respect to d, one obtains

for large m. The term in brackets &ses fiom dispersion.

Chapter 3

EXPERIMENTAL TECHNIQUES

This chapter details the samples studied and the experimental techniques applied.

Initidy a description of the different samples investigated with information on their

growth, material composition and bandgap energies is given. Additional structural

information, obtained fiom transmission electron rnicroscopy, is discussed followed by

some basic processing steps involved in the fabrication of broad area lasers. The last two

sections present the fundamental theory and experimental implementation of the optical

characterization employed: electroluminescence, photovoltage and photoluminescence.

3.1 Sample growth and preparation

Al1 samples were grown by rnolecular beam epitaxy W E ) on a n n-doped GaAs

(100) substrate. The Stranski-Krastanow growth mode was used to produce between one

and five layers of QDs in the active region of a two-step separate confinement

heterostructure (figure 3.1). The structures generally consisted of a thick (-2 pm)

AI@,-& contact layer doped n' - 6x10'' cm-3, followed by a bottom cladding layer of n - 3x10'~ cm-3 doped 4Ga,.+s. The active region is composed of 15 am undoped

Al,,G+-,,As on each side of the Iq&J,,&s QD layer. The symetric p-doped sep-

graded cladding and contact layers with correspondùig doping and matenal

concentrations follow and a 300 rm p'-GaAs cap @ - 3 x 10" cm-3) terminates the

p'-aGa,,As contact layer

pAl$a,+%s top cladding layer

n-Ai,Ga,Jis bottom cladding layer

n'-aGa,& contact layer

n-Ga& substrate

Figure 3.1 Cross-sectional view of the QD laser structure.

Strained iayer + Irb*~o,As

structure. Silicon was used for the n doping, while beryllium was employed for the p

doping. The entire structure was deposited at T - 630 O C , with the exception of the QD section deposited at - 530 O C . Growth was intempted for 2.5 minutes d e r the

deposition of the QD layer; this growth interruption is arbitrary but imf~ortant since in

some strained çystems, an evolution of the QD characteristics such as nmowing of the

size distribution and lowering of the dot density is observed after material deposition [59,

601,

Table 3.1 enurnerates the specific material compositions of six çamples grown

using t h i s procedure. SampIe Ia, ib, Ic and III were fabricated at the National Research

Council Canada using a rnodified V80K VG-Semicon MBE system, wbile samples ZZI

and Llb were rendered at Nortel Technology using a V80H VG-Semicon hWE ~ ç t e m -

Sample

III , I 1

Single layer 4.5 ML y = 0.30 x .t 0.33

Single layer 2.5 ML y = 0.30 x F 0.33

Single layer 2.0 ML y = 0.30 x = 0.33

Single layer 5.0 ML y = 0.35 x .r 0.70

5 layers of dots with 4.5 ML y = 0.35 x 0.70 8 nm &&%.7sAS

spacer layers

Unstrained 5.0 nm thick GaAs QW

Table 3.1 Material composition of the various lasers studied ML stands for monolayei.

40

Samples la-c are al1 single QD Iayer laser structures with different amounts of

deposited materid. They are used to study the ernission characteristics of the QDs,

wetting layers and bbamers. Samples Ua&b have an improved camer confinement

resulting fiom the higher potential barriers (figure 3.2). IIb is used to study the laser

properties observed when more îhan one stack of layers is present in the active region.

Sarnple LU is a reference GaAs/AlGaAs QW laser. The confîning potentials are drawn in

figure 3.2 for samples 1 and 11 161-631. Table 3.2 displays the bandgap energies and -

conduction band offsets of the different materials contained in the heterostructures. The

conduction band offsets (AV) correspond to - 70% for A l W A l G a A s systems and - 65% for AlGaAdGaAs based systems [64, 651. The lattice mismatch between

AJ,,,~,As and Al,,Gz+,,,As is - 3.2 % [63, 661; this tende strain produces a decrease in the bandgap compared with unstrained materials.

Figure 3.2: Schematic mergy-band diagram of (a) samples la-c, and @) samples IIa&b.

Activ Buffer layer Cladding Contact e layer layer

Table 3.2: Bandgaps and conduction band offsets at mom temperature in eV. The QD and contact layer bandgap values do not include the effecîs of strain.

To measure the QD structural characteristics of the various sampies, cross-

sectional transmission electron microscopy (TEM) was perfonned Figure 3 -3 reveals

çamples having a high density of InAlAs islands, with a base diameter of - 20 nm and a thickness of - 5.0 nm. The WLs have a thickness of 2-3 am. These structurai characteristics are comparable to the ones obtained with sùnilar self-assembled dots

WIiere other fundamental studies were performed [67, 681. Figure 3 . 3 ~ shows the cross-

sectionai TEM of sample Ilb, where the 5 stacks are clearly observed and demonstrate

vertical self-aliment of the dots caused by the interacting strain fields induced by the

dots which give nse to a preferred direction in the In migration [69, 701. The dot

dimensions increase in the upper layers in a correlated growth regirne. This vertical self-

assembling is only observed in samples were the spacer layers are thin Oess than - 30 ~ 9 1 -

The TEM micrographs aiso show that the growth &ont retums to a pIanar mode

after only a few nanometers of deposited MO,G5b,,As above the quantum dots to

produce an atomically flat interface at the upper Alo,Ga,,,5Asl~Ga,~,As heterojunction.

The estimated dot dimensions and densities obtained &om the cross-sectional TEMs are

displayed in table 3.3. Sample la's TEM micrograph QD features were not clear enough

to d1ow quantification of the QD density.

Figure 33: TEM cross-section view of the active region of the sarnples, which reveals the ~~~~& QDs (dark) at the center of the A I O 3 ~ - 7 5 & (pale), and with the Alo25G~.7&/A1yGal-y& interface @ne above and below). (a) Sample fa with 4.5 ML of deposited material, @) sample Lla with 5.0 ML, and (c) sample Ilb, the stack of 5 QD layers with 4.5 ML deposited.

QD density Average QD QD heights base diameters

Iir / Notmeasured - 20 6.3 + 1.0

Table 3 3 Estimatecl QD dimensions obtained from cross-sectional TEM aspect d o measurements,

Secondary ion mass spectroscopy (SIMS) analysis was performed on sample LIb.

Doping level results showed beryllium dif i ion, the p-dopant use& al1 the way through

the intrinsic region. This dopant diffusion in the active region was expected to affect the

performance characteristics of the lasers, and therefore the intrinsic region was widened

in the subsequent growth of sample na (LL3 was grown before II@.

The laser structures were processed into broad area lasers with two cleaved

uncoated facets to form a laser cavity. A - 2 cm2 wafer piece was cleaned using organic cleaners, hydrochloric a d . , and ammonium hydroxide. The p-doped side of the structure

was coated in photoresist with a stripe pattern mask over if which was then exposed to

ultraviolet light and subsequently etched, Ieaving ody the s ~ p e design. Mer this, 25

nm of titanium, 55 nm of platinun, and 3 00 nm of gold were evaporated onto the sarnple,

and this was followed by a metal lift-ofX The metal stripes were used as the positive

electricd contacts during the experiments; these had widths of 4O,6O, 100, 150, and 200

m . At this point, the metals used to protect the semiconductor material beneath them,

the top 0.6 pm of GaAs, and the AlGaAs p Iayers were etched away. This etch prohibits

current spreading dong the laterd direction of the laser. The GaAs substzate was then

thinned fiom 600 p m (samples Lla and Ilb) or 450 p m to - 150 p m for easy cleaving, and 25 IIM of nickel, 55 nm of germanium, and 80 nm of gold were evaporated at the base of

the sample and were used as the negative electrical contact. The processed samples were

cleaved into 400 pm-1250 pn wide strips, and each strip holding 5-10 broad area lasers.

The strips were then bound on laser diode mounts with a thmally activated, electrically

conduchg epoxy which provided the negative contacf while gold bonding of the top

metdlization strip provided the positive contact.

In electroluminescence (EL), electrons and holes are injected elec&ically into a

sample and emit a photon after recombination. In a quantum dot laser structure, the

carriers are injected into the bamer material, and diffuse to the vicinity of the quantum

dots. At this point, the carriers therrndize through phonon emission a d o r carrier-carrier

(Auger) interaction fkom a continuum of barrier states, to the WL, and subsequently to

the discrete states of the quantum dots where they eventuaily recombine radiatively.

Band-to-band recombination follows the selection d e s stated in section 2.4. Tbis was

the main technique utilized to characterize die samples since electncal injection

experimentç provide very clear r e d t s in many layered heterostmctures.

Figure 3.4 illustrates an EL set-up. The sample was placed in an optical cryostat

that kept its temperature constant and allowed for electrical contacts. Under forward

bias, electrons and holes were injected electrically into the semiconductor laser where

they recombined in the active region producing photons. The luminescence was

collimated and focussed by a lem system into the entrance slit of a spectrometer. The

emitted light spectrum was then dispersed by a grating and detected with an appropriate

photodetector. The detected signal was digitized and stored in a cornputer.

The typical apparatus consisted of a liquid helium-cooled optical cryostat -

equipped with a heater and temperature controller for measurements between T = 5 K and

T = 300 K with an uncertainty of k 2 K, or a liquid nitrogen-cooled opticd cryostat for

measurements at T = 77 K. The QD lasers were excited using a Hewlett Packard 214B

pulsed power supply driven at a fiequency of 100 Hz and having 10 psec square pulse

widths. Voltages were measured using a Tekonix TDS 320 oscilloscope. The inset in

figure 3.4 shows the electrical circuit employed to measure the potential merence. The

samples in the cryostats were mounted on a cold finger in thermal contact with the

cooling liquid.

In the case of the helium-cooled cryostat., a 0.66-111 spectrometer equipped with a

600-grooves/mm grating dispersed the light onto a Spectmm One CCD array by SPEX

Industries. The CCD array used a parallel detection scheme with a window range of 118

nm over 1024 pixels when using the 600-groves/mm grating. A luminescent Iine having

a FWHM of 3 pixels on the CCD detector leads to a spectral resolution of 0.35 nm, which

translated to an energy resolution of 0.9 meV at 700 nm.

In the case of the liquid nitrogen-cooled cryostat, a 0.67-m spectrometer was used

with a United Detector Technology PIN 10D Si photodiode for strong luminescence

sipals and a Hamamatsu R928 photomultiplier tube for weaker signds. A dispersion of

- 1.2 d m was obtained with a 1200 groovedmm gratuig, giving an energy resolution of 3 meV at 706 m. The signal was d y z e d with the help of a Stanford Research

Systems SR8 10 DSP lock-in amplifier. The unceaainty on the detected signal is

determined by evaluating the intensity changes in a part of the spectnim that has no

features. This would correspond to a random uncertainty of f 0.05 on the noisy spectnim

in figure 4.1 and to values equivalent to the trace width in figure 4.3.

To lock-in amplifier,

Fiiter

. - - -

Lens 1

cornputer, etc.

1

1 Spectrometer

wires for EL SampIe

Figure 3.4 Experimental set-up for electroluminescence and photoluminescence. Show at the bottom of the figure is the electricd circuit used for powering the QD lasers.

For the lasing output characteristics of the devices, a Newport 840 optical power

meter was placed at the exit window of the cryostat. This allowed the measurement of

the total output power as a h c t i o n of the current injected into the device. A systematic

memement uncertainw of - 10 % arises nom a partial light reflection in the cryostat window and fkom a possible clipping of the laser beam due to the small window

diameter. This uncertainty is not taken into account Ui the calcdations. The residual

contact resistance has an uncertahty of - 10 %. This value is obtained f?om the linear regession of the lasers 1-V plots. The meamernent uncertainty combined with the

r

residual contact uncertainty resdts in systematic uncertainties of - 15 % on e x t a a l - efficiency values. The curve shape is still valid since random uncertainties due to

electronic instruments such as oscilloscope, multirneters and power meter are less than 2-

3 % total.

The uncertainty on the threshold curent density is domùlated by a possible

current spreading dong the lateral direction (x-y) of the metal gate and the effective laser

width becomes greater than the actual gate width [SOI. This systematic uncertainty can

be estimated to be - 10 % and is not taken into account in the calcdations. The random unceaainty due to electronic hstmmentation c m be estimated at less than 5 %.

3.3 Photovoltage and photoluminescence

Some of the samples where studied by photovoltage (PV) and photoluminescence.

Photoluminescence is the radiative process by which a material emits a photon f i e r

recombinaiion of thermalized photo-created electron-hole pairs. Photovoltage is a

scanning technique sensitive to direct changes in the optical piopeaies due to

modifications in the absorption coefficient related to the various energy levels. This

technique cm give useful information on the quantum dots as well as higher energy

levels fiom the w e h g layer and the barrier materials.

The PV experimental set-up (figure 3.5) consisted of a hingsten filament light

source dispersed with a spectrometer; the monochromatic beam exited the spectrometer,

went through a chopper, and was focused with two lenses on the sample through one of

the optical windows of the cryostat. The laser sample was used as a light detector, and .

the PV was measured by standard synchronous techniques. The measurements

doue with equipment desciibed in the electroluminescence section.

Crvos tat

Lens 2 Chopper / Slit

were

Electricai wires for PV

Figure 3.5 Exp&ental set-up used for photovoltage-

The experimental set-up used for PL was very similar to the EL set-up described

earlier (see figure 3.4). In this case, a filtered laser beam, at an energy larga than the

materials bandgap value, was used to excited the sample. Experiments were done with a

continuous wave argon ion laser at Lc = 514.5 nm. For thick sampfes with a significant

nurnber of layered materials such as the ones studied here, PL spectra were often

ambiguous shce interferencc f i g e s were present due to the device waveguide

configuration, and sbce luminescence intensities fiom the different mat e n d layers varied

greatly depending on the position and angle of the incident laser light.

Chapter 4

RESULTS AND DISCUSSION

E~ectrolumuiescence spectra of samples with different deposited amounts of

hAlAs are acquired to characterize the spontaneous and stimulated emissions onginating

fkom QDs, WL, and b h e r material in the laser structures. In addition, the structures are

verified using photoluminescence and photovoltage. A dependence on the co-g

potential for the temperature characteristic of the threshold current

is observed when comparing samples with dinerent b d e r layer confining energies- The

specific properties of multi-stack QD structures are shown and subsequently discussed

Operating characteristics of QD lasers, such as peak power output, external quafl-

efficiency and temperature dependence of threshold current density, are also presented

These results are systematically compared with control QW lasers.

The fist part of this work provides experimental evidence that stimulated

emission can be obtained fkom QDs. The three samples having different deposited

amounts of InAlAs, but the same confining potentials: samples Iu, Ib and Ic are discussed

in this section. Samples In and I b were pocessed into 60 Pm by 400 ~ x n broad area

Iasers.

4.1.1 Spontaneous emission from quantum dots

As shown on the TEM in figure 3.3% sample In has a relatively high QD density.

If we assume a QD coverage of - 50% of the plane (which is roughly that estimated from the TEM cross section), the number of QDs which are present in the resonating cavity (60

p u x 400 pn) can be estimated at - 10'. At T = 77 K, for very low injection currents, the EL emission of this sample is centered at a wavelength A. = 725 nm (1.7 1 1 eV) with a

- 54 meV full width at haif maximum (FWEh/T) Gaussian iineshape (figure 4.1). This emission spectnim is similar to the PL spectnim obtained with nominally equivalent QDs

grown in an n-i-n structure designed for a separate optical investigation [71]. It is also

comparable to the PL spectra obtained fiom self-assembled QDs displaying efficient

photocarrier thermalization with no observable excited-state emission under low

excitation intensiw (figure 2.2). The inhornogeneously broadened Gaussian EL Line

shape is therefore attnbuted to the emission fkom injected carriers thennalized in the

statistically distributed ground states of the probed QDs.

A closer look at figure 4.1 reveals a slight asymmetry in the EL peak broadening

to higher energies indicating the possibility that some state-filling effects occur at very

low injection current densities. As described in section 2.1, state-filluig effects are due to

the fact that only two carriers can populate the ground state level in a QD. Under low

excitation intensities, only the ground state level of the QDs are popuiated owing to a fast

intersublevel relaxation nom the higher energy Ievels to the lowest energy level leaving

only radiative recombination nom the QD ground states. As more caniers are injected

into the QD structure, a progressive saturation of the QD ground states occurs, leaving

the higher energy states populated Therefore, unda such high injection, radiative

recombination from excited states is observed as the intersublevel carnier relaxation

toward the lower level is siowed due to the reduced nmber of available final states [22,

35-37, 561. If the uihomogeneous broadening were less than the intersublevel spacings, -

the state Nling effect would give distinct peaks 2t high injection currents similar to the

ones observed in figure 2.3. For these InAlAs QDs, the inhomogeneous broadening is

larger than the inter-sublevel spacing, so the state flling effect produces a spectnim with

an asymmetric peak shifting towards higher energies as the injection curent is increased

197 301.

Figure 4.1 EL of sample la for very low bias (J= 3 A/cmZ) at T= 77 K.

When large ensembles of QDs are probed, it is not possible to observe the very

sharp homogeneous EL emission line of each individual QD (see figure 2.3, p. 12) 1371.

. To reveal the intrinsic sharpness of the emission fkom each QD, we gated the structure

with an opaque electrode having a small opening (a few square micrometers) in its center.

The detected EL, which onginates f?om a much smaller number of QDs, is shown in the

hi& resolution EL-spectnim of figure 4.2 for various applied voltages. As observed, a

number of sharp spectral feahtres of comparable amplitudes appear with FWHM ranging

from 200 to 500 peV. Each sharp feature corresponds to the EL of a few QDs emitting at

similar wavelengths. The small energy shift of individual lines (redshift) observed with

increasing voltage c m be attributed to the quantum-confhed Stark effect [71]. The

sharpness of the lines demonstrates the zero-dimensional nature of the energy levels in

which the electncally injected carriers thermalize and recombine.

' L ' " ' 1 " " 1 " " 1 - . - -

1 .71 5 1.720 1.725 1.730 1 . i35 EMERGY (eV)

Figure 4 2 Low-temperature (42 K) EL spectra obtained at various applied voltages on sample la gaîed with an opaque electrode having an opening of a few square micrometers that is used to delineate the number of QDs probed. nie sharp emission lines reveal the discrete nature of density of states of the individual dots.

4.1.2 Stimulated emission h m quantum dots

The 77 K EL emission fkom a broad area laser structure under fornard bias is

shown in figure 4.3. For currents < 10 mA, the EL line shape is Gaussian and centered at

725 nm Oowest curve of figure 4.3a is the curve displayed in figure 4.1). With increasing

current, the emission peak becomes asymmetric and shifts to higher energies. For

currents just below lasing threshold, the spectral distribution nariows progressively and at

- 175 mA (cunent densities J - 700 A/cm2), a stimulated emission peak appears on top of the asymmeîric EL peak As the current is increased M e r , the laser cavity supports

multiple longitudinal modes, and several sharp k i n g peaks appear near 707 nm (1.754

eV). These can be seen more clearly in the semilogarithmic plot of figure 4.3b for a

current of 600 mA ( J = 2500 A./cm2), and a peak laser output power of 44 mW. These

wavelengths are in the fa red spectnim and can be seen by eye. The output beam is

spatially collimated and has a considerable divergence due to the very narrow active

region. This stimulated emission is attn'buted to the QDs.

1 . 1 1 t t . 1 1

10m0, b) l ( i ) ï = 7 m A (ii) 1 = 5 0 m A z? (Üï) I = l O O XDA '3 Mi (iv) 1 = iî5mA 9 (v) I= 175 mA & 1

(vii l = a D O l n A Y 3 (viï) I = Z S mA

(Mi) 1=600 mA -

Figure 4 3 The (a) EL and @) multimode 1-g specmim at 77 K of sample ia for forward biases. The QD structure processed into a broad area laser emits in the red wavelengths (1.754 eV). The emission changes fiom Fontaneous to stimulaîed as the injection current is increased above a threshold of 175 mA (Jh - 700 Ncm-). The optical gain for the various lasing modes is provided by a different QD subset in the ensemble of - 10' QDs in which carriers are injecte&

For each longitudinal mode, a dinerent subset of the QD ensemble provides the

optical gain. The - 40-meV blue shift observed between the low-current Gaussian EL spectra and the asymxnetnc spectra at threshold is most likely attributable to a change

fkom ernission nom the QD ground states, at' low currenf to emission from the QD

excited states, at threshold current where the Iarger number of injected carriers are filling

the QD ground states. The 40-rneV shifi would then correspond to the sum of the

electron and the hole intersubievel spacings between hKo adjacent allowed optical

transitions. This is consistent with similar state fiIlhg e£fects observed in the PL spectra

of QDs excited optically [9, 30, 3 1, 35, 601. Furthemore, the small higher energy peak

observed at R = 724 nm (1.713 eV) under lasing conditions (figurc 4.3b) matches the

peak position of the ground-state emission that is observed at very low inje